The exponential Diophantine equation (3am2−1)x+(a(a−3)m2+1)y=(am)z(3am2−1)x+(a(a−3)m2+1)y=(am)z(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z

Nai-juan DENG; Dan-yao WU; Ping-zhi YUAN

Makale detayları

The exponential Diophantine equation (3am2−1)x+(a(a−3)m2+1)y=(am)z(3am2−1)x+(a(a−3)m2+1)y=(am)z(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z

Yazarlar:

Nai-juan DENG | Dan-yao WU | Ping-zhi YUAN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 5, pp.2561-2567

Belge Tipi:

Makale

Yayın Tarihi:

9/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000745552

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

Let a, ma, ma,\ m be positive integers such that am≢0(mod3),2∤aam≢0(mod3),2∤aam\not\equiv0\pmod{3}, 2\nmid a, and a>3a>3a>3. We prove that the exponential Diophantine equation (3am2−1)x+(a(a−3)m2+1)y=(am)z(3am2−1)x+(a(a−3)m2+1)y=(am)z(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z has only the positive integer solution (x,y,z)=(1,1,2)(x,y,z)=(1,1,2)(x,y,z)=(1,1,2).

Makale detayları

The exponential Diophantine equation (3am2−1)x+(a(a−3)m2+1)y=(am)z(3am2−1)x+(a(a−3)m2+1)y=(am)z(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z

Yazarlar: Nai-juan DENG | Dan-yao WU | Ping-zhi YUAN

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 5, pp.2561-2567

Belge Tipi: Makale

Yayın Tarihi: 9/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000745552

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Nai-juan DENG | Dan-yao WU | Ping-zhi YUAN

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 5, pp.2561-2567

Belge Tipi:

Makale

Yayın Tarihi:

9/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000745552

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098